Optimism and commitment: An elementary theory of bargaining and war

We propose an elementary theory of wars fought by fully rational contenders. Two parties play a Markov game that combines stages of bargaining with stages where one side has the ability to impose surrender on the other. Under uncertainty and incomplete information, in the unique equilibrium of the game, long confrontations occur: war arises when reality disappoints initial (rational) optimism, and it persist longer when both agents are optimists but reality proves both wrong. Bargaining proposals that are rejected initially might eventually be accepted after several periods of confrontation. We provide an explicit computation of the equilibrium, evaluating the probability of war, and its expected losses as a function of i) the costs of confrontation, ii) the asymmetry of the split imposed under surrender, and iii) the strengths of contenders at attack and defense. Changes in these parameters display non-monotonic effects.

Class-size Reduction Policies and the Quality of Entering Teachers

State-wide class-size reduction (CSR) policies have typically failed to produce large achievement gains. One explanation is that the introduction of such policies forces schools to hire relatively low-quality teachers. This paper uses data from an anonymous state to explore whether teacher quality suff ered from the introduction of CSR. We find that it did, but not nearly enough to explain the small achievement effects of CSR. The combined fall in achievement due to hiring lower quality teachers and more inexperienced teachers is small relative to the unrealized gains. Furthermore, between-school diff erences in the quality of incoming teachers cannot explain the poor estimated CSR performance from previous quasi-experimental treatment-control comparisons.